Multiple Coordinate Spaces - 3D Math Primer for Graphics and Game Development - page 85

Figure 3.2
Object, upright, and world
space.
Why is upright space interesting? To transform a point between object
space and upright space requires only rotation, and to transform a point
between upright space and world space requires only a change of location,
which is usually called a translation. Thinking about these two things
independently is easier than trying to cope with them both at once. This is
Figure 3.3
Conversion between world and upright space via translation; upright and object space are
related by rotation